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2.3 – Introduction to Functions. Objectives: State the domain and range of a relation, and tell whether it is a function. Write a function in function notation and evaluate it. Standards: 2.8.11.S. Analyze properties and relationships of functions. - PowerPoint PPT Presentation
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2.3 – Introduction to Functions
• Objectives:– State the domain and range of a relation, and
tell whether it is a function.– Write a function in function notation and
evaluate it.
• Standards: – 2.8.11.S. Analyze properties and relationships
of functions.– 2.8.11.O. Determine the domain and range of
a relation.
Warm Up:
- 7 3 16
- 1.44 - 8 0.001
The domain of a function is the set of all possible values of x (the inputs).
The range of a function is the set of all possible values of y (the outputs).
Examples: State whether the data in each table represents a function.
a). b).
a).
b).
More Examples:
x y
3 4
3 5
5 -4
6 3
Ex. 1c
NO
x y
2 2
4 3
6 4
8 5
Ex. 1d
YES
c).
Not a function. It does not pass the vertical line test.
d).
Not a function. It does not pass the vertical line test.
The domain of a function is the set of all possible values of x (the inputs).
The range of a function is the set of all possible values of y (the outputs).
Domain: {-2, 0, 3, 8}Range: {-26, -6, 24, 74}
Domain: {-6, -4, 2, 3}Range: {7, 12, 19, 39}
• III. A function is a special type of relation. A relationship between two variables such that each value of the first variable is paired with one or more values of the second variable is called a relation.
Ex 4.
D:
R:
b.
2x
0y
State the domain and range of eachgraphed.
c.d.
D: x > -2
R: y > -1
Open circle
Functions and Function Notationy = 2x + 5 → f (x) = 2x + 5
If there is a correspondence between the domain
and range that is a function, then y = f(x), and (x, y)
can be written as (x, f(x)). The number represented by f(x) is the value of the function f at x.
The variable x is called the independent variable.
The variable y, or f(x), is called the dependent variable.
p. 108: #17-35 odd (answers in back of book)
p. 108: #17-35 odd (answers in back of book)
pp. 108 &109: 37-47odd
p. 109: #51, 53, 57
Homework